Mister Exam
Other calculators
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How to use it?
- Equation:
-
Equation -7x=4
-
Equation x^2-6=0
- Equation x^2-x-90=0
-
Equation -9x=36
- Express {x} in terms of y where:
- -6*x-11*y=-20
- -15*x+7*y=1
- -10*x+4*y=3
- -8*x-16*y=-1
-
Identical expressions
- x^ two -x- ninety = zero
- x squared minus x minus 90 equally 0
- x to the power of two minus x minus ninety equally zero
- x2-x-90=0
- x²-x-90=0
- x to the power of 2-x-90=0
- x^2-x-90=O
-
Similar expressions
- x^2-x+90=0
- x^2+x-90=0
x^2-x-90=0 equation
The teacher will be very surprised to see your correct solution 😉
The solution
Detail solution
This equation is of the form
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -1$$
$$c = -90$$
, then
Because D > 0, then the equation has two roots.
or
$$x_{1} = 10$$
$$x_{2} = -9$$
a*x^2 + b*x + c = 0
A quadratic equation can be solved
using the discriminant.
The roots of the quadratic equation:
$$x_{1} = \frac{\sqrt{D} - b}{2 a}$$
$$x_{2} = \frac{- \sqrt{D} - b}{2 a}$$
where D = b^2 - 4*a*c - it is the discriminant.
Because
$$a = 1$$
$$b = -1$$
$$c = -90$$
, then
D = b^2 - 4 * a * c =
(-1)^2 - 4 * (1) * (-90) = 361
Because D > 0, then the equation has two roots.
x1 = (-b + sqrt(D)) / (2*a)
x2 = (-b - sqrt(D)) / (2*a)
or
$$x_{1} = 10$$
$$x_{2} = -9$$
Vieta's Theorem
it is reduced quadratic equation
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -90$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -90$$
$$p x + q + x^{2} = 0$$
where
$$p = \frac{b}{a}$$
$$p = -1$$
$$q = \frac{c}{a}$$
$$q = -90$$
Vieta Formulas
$$x_{1} + x_{2} = - p$$
$$x_{1} x_{2} = q$$
$$x_{1} + x_{2} = 1$$
$$x_{1} x_{2} = -90$$
Sum and product of roots
[src]
sum
-9 + 10
$$-9 + 10$$
=
1
$$1$$
product
-9*10
$$- 90$$
=
-90
$$-90$$
-90